We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices.To obtain these sufficient conditions,we construct new ...We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices.To obtain these sufficient conditions,we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices.As applications,we provide a unified way to produce inequalities for many combinatorial polynomials,such as the Eulerian polynomials,Schröder polynomials,and Narayana polynomials.展开更多
基金This work was supported in part by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China(Grant Nos.11522110,11971249).
文摘We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices.To obtain these sufficient conditions,we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices.As applications,we provide a unified way to produce inequalities for many combinatorial polynomials,such as the Eulerian polynomials,Schröder polynomials,and Narayana polynomials.
